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Teoriya Veroyatnostei i ee Primeneniya, 1979, Volume 24, Issue 4, Pages 858–865
(Mi tvp2913)
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This article is cited in 6 scientific papers (total in 6 papers)
Short Communications
On the probabilities of moderate deviations for sums of independent random variables
N. N. Amosova Leningrad
Abstract:
Let $X_1,X_2,\dots$ be a sequence of independent identically distributed random variables and $\sigma>0$. Put
$$
F_n(x)=\mathbf P\biggl\{\sum_{i=1}^nX_i<x\biggr\},\qquad\Phi(x)=(2\pi)^{-1/2}\int_{-\infty}^x e^{-t^2/2}\,dt.
$$
Necessary and sufficient conditions are found for the validity of the relation
$$
1-F_n(x\sigma\sqrt n)=(1-\Phi(x))(1+o(1)),\qquad 0\le x\le c\sqrt{\log n},\qquad n\to\infty.
$$
Received: 26.12.1977
Citation:
N. N. Amosova, “On the probabilities of moderate deviations for sums of independent random variables”, Teor. Veroyatnost. i Primenen., 24:4 (1979), 858–865; Theory Probab. Appl., 24:4 (1980), 856–863
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https://www.mathnet.ru/eng/tvp2913 https://www.mathnet.ru/eng/tvp/v24/i4/p858
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